Question

Glven the following expressions: A. 5³.5-⁴ B. 3⁵/3-⁶ C. (1/4)³.(1/4)² D. (-7)⁵/(-7)⁷Part 1: Use operations of exponents to slmpllfy each expression (A-D). Include your work in your final answer. Part 2: For each simplified expression (A-D), tell whether or not the expression has a value between 0 and 1.

Answer 1

Step 1:

To answer each of the questions, you will apply the multiplication and division laws of the exponent.

$\begin{gathered} \text{Multiplication law} \\ \text{If m}^n\text{ }\times m^t=m^{n+t} \\ \text{Division law} \\ \text{If m}^n\text{ }\frac{.}{.}m^t=m^{n-t} \end{gathered}$

Step 2:

$\begin{gathered} a)5^3\text{ }\times5^{-4}=5^{3-4} \\ =5^{-1} \\ =\text{ }\frac{1}{5} \\ \end{gathered}$